John Mueller offered points on what you should do at the start of removal request.

This tool is useful for removals on other peoples’ websites. You could use this tool if a page has been removed completely, or when it was just changed and you require having the snippet & cached page removed. If you are the webmaster of the website, then applying the Webmaster Tools URL removal feature is quicker& less complicated.

Just in case web pages was not taken off, you can makes use of the same tool, Making use of the Webmaster Tools URL removal feature is very simple for the real owners of the website. Visit the tool and type in a phrase that no longer appears to the live web page and Google will get it from there.

To get more detailed & information about this new tool please read the most recent post on the Official Google Webmaster Central Blog.